What is the derivative of (2(3x^4-5)/(x^3)) ?

The derivative of (2(3x^4-5)/(x^3)) is (6(x^4+5))/(x^4)

What is the first derivative of (2(3x^4-5)/(x^3)) ?

The first derivative of (2(3x^4-5)/(x^3)) is (6(x^4+5))/(x^4)

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\frac{d}{d x} (\frac{2 ( 3 x ^{4} - 5 )}{x ^{3}})

\frac{6 ( x ^{4} + 5 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{2 ( 3 x ^{4} - 5 )}{x ^{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{3 x ^{4} - 5}{x ^{3}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 2 \cdot \frac{\frac{d}{d x} ( 3 x ^{4} - 5 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 3 x ^{4} - 5 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (3 x^{4} - 5) = 12 x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

= 2 \cdot \frac{12 x ^{3} x ^{3} - 3 x ^{2} ( 3 x ^{4} - 5 )}{( x ^{3} ) ^{2}}

Simplify

2 \cdot \frac{12 x ^{3} x ^{3} - 3 x ^{2} ( 3 x ^{4} - 5 )}{( x ^{3} ) ^{2}} : \frac{6 ( x ^{4} + 5 )}{x ^{4}}

= \frac{6 ( x ^{4} + 5 )}{x ^{4}}

(- 2.2) (0)

y = 6 x^{2}, y = x^{2} + 4

\frac{d}{d x} (3 + x^{2})

\frac{\partial}{\partial y} (arctan (x))

\frac{d}{d x} (2 (x - 2 π))

What is the derivative of (2(3x^4-5)/(x^3)) ?
The derivative of (2(3x^4-5)/(x^3)) is (6(x^4+5))/(x^4)
What is the first derivative of (2(3x^4-5)/(x^3)) ?
The first derivative of (2(3x^4-5)/(x^3)) is (6(x^4+5))/(x^4)